1. Introduction

Combining coherent laser beams is an important and challenging area of laser science. Achieving a single output of both high-power and high-brightness from many moderate-power lasers as well as coherent control of beam deflection without mechanical movements are goals which, if achieved, promise a great number of scientific and industrial applications. Many researchers have investigated phase-locked laser arrays with versatile methods to obtain a diffraction-limited beam at the far field [1–4]. High-power operations with high addition efficiencies are often limited because of the small threshold difference among the supermodes and the increased cavity loss. Coherent laser arrays phase-locked to form a single beam at the near field with all-waveguide configurations are attractive owing to their inherent fine beam quality and low-loss property.

Kozlov et al. [5] reported coherent beam combining of two fiber lasers by using one half of a 2 × 2 fused-fiber coupler. In an overcoupled regime a single beam is formed on the common cleaved facet at the center of the coupler. Here we report that coherent addition of N fiber lasers can be realized even by use of an N × N fused-fiber coupler as the combiner. Nearly N-times higher output power was successfully obtained as a single-beam fiber output from one of the N fiber ports in the cases of N = 2 and N = 4. Both length difference among the laser arms and loss imbalance among the ports originate the selective excitation of the supermodes to output a coherently added single beam from one of the ports. We can achieve a significant amount of threshold difference among the supermodes simply by applying losses in the ports except for the target port that ensures high addition efficiency even far-above threshold as well as sophisticated output-port switching capability. These outstanding features promise versatile applications.

2. Coherent addition of two fiber lasers

The experimental setup of the coherent fiber laser array with two lasers is shown in Fig. 1. The pump source was a self-made phosphosilicate fiber Raman laser with a maximum power of 4.7 W at 1484 nm [6,7]. The output was split into two by a 50:50 fiber coupler and each pumped one of the fiber lasers (laser A/B) with a 2.05-W power by means of a 1484/1557-nm wavelength-division multiplexing (WDM) coupler. The gain fibers were 6-m-long single-mode Er-doped fibers (Nufern Model EDF555), and the fiber of laser A was looped into a polarization controller. Each laser cavity was formed by a fiber Bragg grating (FBG) (R ∼ 99% with a FWHM of ∼0.6 nm centered at the Bragg wavelength of ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$ = 1556.95 nm for FBG A and ${{\lambda }^{\text{Bragg}}}_{\mathrm{B}}$ = 1557.15 nm for FBG B) and 3.4% Fresnel reflection at the output cleaved facet. We were able to tune ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$ to longer wavelengths by stretching the fiber. In the case of an independent array (dashed lines in Fig. 1), the maximum output powers of lasers A and B were P _A= 1.36 and P _B = 147 W, respectively. The small imbalance of the power is due to the internal loss difference between the WDM couplers. When both lasers were connected by a 50:50 fused-fiber coupler, the outputs became unequal but one sided to one of the two fiber ports (Port A/B). The power distribution was sensitive to the conditions of the cleaved facets and bending losses of both ports. We found that higher power was always emitted from the port with a lower loss. In one case we obtained the most unbalanced output powers of P _A = 2.57 and P _B = 0.17 W after adjustment of the polarization controller, which corresponded to an addition efficiency of more than 90%. Note that cavity length control was not implemented. The evolution of output powers in both cases of the independent and coupled array is shown in Fig. 2, clearly indicating no evidence of any nonlinear effects or decrease in addition efficiency. Both outputs of the coupled array have almost the same spectral shape around the middle of the spectra of the independent array (inset in Fig. 2). Figure 3 shows the spectral and power changes of the outputs from ports A and B when we tuned ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$ from 1556.95 to 1558.20 nm by stretching FBG A. The coupling state was kept for the detuning δλ = |${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$-${{\lambda }^{\text{Bragg}}}_{\mathrm{B}}$| less than 0.5 nm, which is nearly equal to the FBG bandwidth. The addition efficiency was almost constant in this region. For δλ > 0.5 nm, both spectra exhibited perfectly separated double-peak shapes at the two Bragg wavelengths and the powers were distributed almost equally in both ports, indicating an incoherent array without any coupling.

Applying additional loss in the fiber ports can reverse the higher-power port of the coupled array. Figure 4 shows the change in output powers with increased curvature of the looped part of the initial higher-power port A. In this case ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$ = ${{\lambda }^{\text{Bragg}}}_{\mathrm{B}}$ = 1557.15 nm, which was used throughout the following experiments. In the transition region with the applied loss from ∼6% to 10% the powers were unstable and competed with each other, but the powers were sufficiently stable outside this region. The total power was reduced in the transition region but almost recovered when a large portion of the output power was transferred to port B.

 

Fig. 1. Experimental setup of the fiber laser array. The dashed lines indicate the independent array without a 50:50 fused-fiber coupler. PC, polarization controller; EDF, Er-doped fiber.

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Fig. 2. Dependence of the output powers on the pump power launched on each WDM coupler. P _A (red) and P _B (blue) of the initial independent array (open circles) and those of the coupled array (filled circles) are shown. Inset: spectra of the port A (red) and port B (blue) outputs for the independent array (dashed curves) and the coupled array (solid curves) at maximum pumping.

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Fig. 3. Change with tuning ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$. (a) Spectra of port A (red curves) and port B (blue curves) outputs. The positions of ${{\lambda }^{\text{Bragg}}}_{\mathrm{A}}$ and ${{\lambda }^{\text{Bragg}}}_{\mathrm{B}}$ are indicated by red and blue dashed lines, respectively. (b) P _A (red filled circles), P _B (blue filled circles), and P _A+P _B (filled squares).

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Fig. 4. Dependence of P _A (red filled circles), P _B (blue filled circles), and P _A+P _B (filled squares) on the additional loss applied to port A.

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3. Coupling mechanisms and characteristics

The behavior described above can be understood with the supermode theory [8]. If an array is composed of two identical cavities, only in-phase and/or out-of-phase supermodes will oscillate, and the output power should always be equivalent in both ports. The array reported here, however, was composed of cavities with different fiber lengths, which is inevitable when one cuts and splices fibers and fiber components. We found that the length difference ΔL = L _B - L _A between arm A and arm B (left-hand side parts from the 50:50 fiber coupler in Fig. 1) often amounted up to more than ten centimeters. In such cases, wavelengths that satisfy the condition βΔL = (m + 1/2)π (m is an integer and β is the propagation constant) give two constructive supermodes with a single output from one of the ports by the coherent addition of fields from the gain media. We refer to these modes as Y modes (Y _A and Y _B with the axes corresponding to port A and port B, respectively) because the character Y is a good representation of the energy flow in the laser array. In our experiments such wavelengths can always exist within the bandwidth of the FBGs because of the dense longitudinal-mode (<10-MHz mode spacing) feature as well as small ΔL in comparison with the cavity length (Vernier effect), and any fine adjustments of the fiber length become unnecessary. The loss imbalance between the two ports places one of the Y modes at the lowest threshold among the possible modes including in-phase and out-of-phase modes, and the preferable single output is generated. The unstable behavior and reduction of the total power in the transition region in Fig. 4 indicate a mode competition that is due to loss balancing and the resultant increase of the net cavity loss, respectively.

Lyndin and his co-workers reported a similar experimental apparatus in 1994 [9]. They connected two fiber lasers by a clad-polished fiber coupler, placed an R = 95% mirror at one of the fiber port exits, and obtained ∼200-μW output power from the mirror port with an addition efficiency of ∼95%. This result is well understood by the presented Y-mode picture: the output power is concentrated in the lower threshold mode with the mirror. Lyndin et al. also indicated the importance of arm-length difference for automatic satisfaction of the constructive interference condition. However, details of the coupling behavior were not made clear.

We studied the longitudinal-mode structure of our coupled array by measuring the beat spectra of both port outputs with a fast photodetector and a radio-frequency spectrum analyzer (Anritsu Model MS2661C). The fiber lengths were estimated to an accuracy of ±1 mm. Figure 5 shows the beat spectra with ΔL = 0.341 m. By assuming the mode index of n = 1.45, we predicted frequency spacing of Y modes to be Δv_Y = c/(2nΔL) = 303 MHz, which is in fairly good agreement with the observed spacing (∼300 MHz) among the peak frequencies in the individual beat packet. By changing ΔL from 0.980 to 0.010 m, we expanded the spacing among the beat peaks in accordance with Δv_Y = c/(2nΔL), whereas the number of beats in one beat packet increased with the almost invariant addition efficiency. The beat spectrum of the port B output is rather complicated. In addition to the main beats at the same positions as those of the port A output, there are side wings with frequency offsets. The latter component can be dramatically decreased if we prevent reflection from the exit facet of port B by splicing an FC/APC connector. The origin of this component could be due to excitation of a different polarization component in the Y _A mode with a slightly different mode index. The return losses of the fiber couplers are less than 10^-4% and no parasitic resonance effects will occur. Suppressing the energy dissipation by preventing reflection or by applying an infinite loss in port B increases P _A and the addition efficiency. For the array with ΔL = 0.341 m, we increased P _A from 2.57 to 2.65 W by immersing the facet in index-matching oil or by crushing the looped part of port B. The addition efficiency amounted to 93.6%.

 

Fig. 5. (a) Beat spectra of the port A output (red curves) and port B output (blue curves) when the Y _A mode was excited at ΔL = 0.341 m. Fine structures of the port B output are smeared out because of limited resolution. (b) Beat spectra with higher resolution.

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The coupled array with infinite loss in one of the ports is equivalent to a Fox–Smith resonator [10,11], which was investigated mainly for single-longitudinal-mode operation of a single laser. Figure 6 shows the line-shape functions g ₁(v) and g ₂(v) defined as the transmittance of a light launched on port A to arm A and to port B (no feedback), respectively, for arrays with ΔL = 0.341 m, L _A = 10.492 M, and l _A = 1.414 M (l _A is the length of port A) [11]. Because the line-shape function of each laser in an independent array (simple Fabry–Perot resonators) has a peak transmittance of T _max= T ₁ T ₂/[1-(R ₁ R ₂)^1/2]² = 0.0145 (R ₁ = 0.99, R ₂ = 0.034, and T _i = 1-R _i), the peak value of 0.00725 in g ₁(v) means a 100% addition efficiency, where the exact double-resonance condition is satisfied. Leakage to port B occurs when the sidebands are excited, as was observed as beat packets in Fig. 5, which explains the main beat component in the port B output and slightly degrades the addition efficiency. The mode spacing of the sidebands in the line-shape functions is given as c/(2nL _av) = 8.56 MHz [L _av = (L _A + L _B)/2 + l _A, the average cavity length], which is in good agreement with the experimental results. Insertion loss of the fiber coupler (∼3%) also reduces the efficiency and could provide an essential factor in the present experiment. The decrease of efficiency caused by the power difference between laser A and laser B as well as the unbalanced branching ratio of the coupler (maximum ±2%) is estimated to be less than 0.2% and is, therefore, negligible.

 

Fig. 6. Line-shape functions g ₁(v) (red curve) and g ₂(v) (blue curve) at the lowest frequency region in the Fox–Smith limit. Characters Y_A indicate the positions of the Y_A modes estimated from the beat spectrum in Fig. 5.

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4. Coherent addition of four fiber lasers

The coherent addition of four fiber lasers has been successfully demonstrated; see the experimental setup in Fig. 7. Each Er-doped fiber laser was equivalent to the laser explained above and coupled with a 4 × 4, 25:25:25:25 fused-fiber coupler. Bragg wavelengths of the FBGs were all approximately 1557.15 nm. Only two were equipped with polarization controllers for practical reasons. Three fiber ports were immersed in index-matching oil to obtain the highest power from the fourth port. The output powers of the initial independent array were 0.68, 0.65, 0.62, and 0.61 W for each pump power of 1.0 W, whereas output power of 2.45 W was obtained from the fourth port of the coupled array, which corresponds to an addition efficiency of as high as 95.6%. Further details of the coupling properties as well as the scalability of the number of fiber lasers are now under investigation.

 

Fig. 7. Experimental setup of the N = 4 fiber laser array. PC, polarization controller; EDF, Er-doped fiber.

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5. Conclusions

Highly efficient coherent addition of N = 2 and N = 4 fiber lasers was achieved with intracavity N × N fused-fiber couplers. Our method for combining multiple lasers has many favorable features such as high addition efficiency, fine switching capability, and an all-fiber configuration that maintains a single transverse mode. Many applications to high-power lasers, laser processing, and optical communications are expected.